Restarting accelerated gradient methods with a rough strong convexity estimate

We propose new restarting strategies for accelerated gradient and accelerated coordinate descent methods. Our main contribution is to show that the restarted method has a geometric rate of convergence for any restarting frequency, and so it allows us to take profit of restarting even when we do not know the strong convexity coefficient. The scheme can be combined with adaptive restarting, leading to the first provable convergence for adaptive restarting schemes with accelerated gradient methods. Finally, we illustrate the properties of the algorithm on a regularized logistic regression problem and on a Lasso problem.